Abstract
We study the collective oscillations in two-band superconducting systems with all possible intra-and interband interactions for arbitrary values of carrier density N0, including low carrier densities, when μ∼Δ. Allowance for processes of scattering of an interband Cooper pair into an intraband pair leads to the emergence of a new excitonic mode in addition to the Bogolyubov-Anderson acoustic mode and an excitonic mode of the Leggett type. The presence of a new order parameter Δ2, in addition to Δ11 and Δ22, and the asymmetric cutoff of integrals lead to the mixing of fluctuations of the phases and amplitudes of the order parameters of different bands. This mixing and the dependence of the order parameters on N0 result in a strong dependence of these two excitonic modes on the carrier density N0.
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